The Application of Kolmogorov’s theorem in the one-default model

Fatima Benziadi; Abdeldjebbar Kandouci

doi:10.36753/mathenot.421459

Research Article

Year 2016, Volume: 4 Issue: 2, 71 - 78, 30.10.2016

Fatima Benziadi Abdeldjebbar Kandouci

https://doi.org/10.36753/mathenot.421459

Abstract

References

[1] Philip E.Protter., Stochastic integration and differential equations. Math.Appl, Second edition, Springer-Verlag, 2004.
[2] H.Kunita., Stochastic flows of diffeomorphisms. Lect.Notes in Math.Vol 1997, Springer-Verlag 1984.
[3] G.Barles., Solution de viscosité des équations de Hamilton-Jacobi. Math.Appl.Vol 17, Springer-Verlag, Paris, 1994.
[4] Bernt Oksendal., Stochastic differential equations. Springer-Verlag, Berlin, Heidelberg, 1985, 1989, 1992, 1995, 1998, 2003.
[5] J.Jacod., Calcul stochastique et problèmes de martingales. Springer-Verlag, Berlin, Heidelberg, New York 1979.
[6] Sheng-wu He, Jia-gang Wang and Jia-an Yan., Semimartingale theory and stochastic calculus. Science Press and CRC press INC, 1992.
[7] G.Constantini, Equations différentielles d’ordre 2, (http://bacamaths.net/).
[8] Monique Jeanblanc, Shiqi Song., Random times with given survival probability and their F-martingale decomposition formula, Stochastic Processes And their Applications, 121(2011).
[9] T.R.Bielecki, M.Jeanblanc and M.Rutkowski., Credit Rist Modelling. Osaka University Press, 2009.
[10] R.J.Elliot, M.Jeanblanc and M.Yor., On models of default risk, Mathematical Finance. 2000.
[11] I.Karatzas, Kardaras.C., The numéraire portfolioinsemimartingale financial models. Finance and Stochastics, 11(4) 447-493 (2007).
[12] T.Jeulin, M.Yor., Nouveaux résultats sur le grossissement des tribus. Ann. Scient. Ec. Norm. Sup. 4t, 11 429-443 (1978).
[13] C.Yoeurp., Décomposition des martingales locales et formules exponentielles. Séminaire de Probabilités, 10 432-480 (1976).
[14] S.W.He, J.G.Wang and J.A.Yan., Semimartingale Theory And Stochastic Calculues Science. Press, CRC, Press Inc 1992.

The Application of Kolmogorov’s theorem in the one-default model

Year 2016, Volume: 4 Issue: 2, 71 - 78, 30.10.2016

Fatima Benziadi Abdeldjebbar Kandouci

https://doi.org/10.36753/mathenot.421459

Abstract

Keywords

Progressive enlargement of filtration, Semimartingale decomposition, Multiplicative decomposition, Credit risk

References

[1] Philip E.Protter., Stochastic integration and differential equations. Math.Appl, Second edition, Springer-Verlag, 2004.
[2] H.Kunita., Stochastic flows of diffeomorphisms. Lect.Notes in Math.Vol 1997, Springer-Verlag 1984.
[3] G.Barles., Solution de viscosité des équations de Hamilton-Jacobi. Math.Appl.Vol 17, Springer-Verlag, Paris, 1994.
[4] Bernt Oksendal., Stochastic differential equations. Springer-Verlag, Berlin, Heidelberg, 1985, 1989, 1992, 1995, 1998, 2003.
[5] J.Jacod., Calcul stochastique et problèmes de martingales. Springer-Verlag, Berlin, Heidelberg, New York 1979.
[6] Sheng-wu He, Jia-gang Wang and Jia-an Yan., Semimartingale theory and stochastic calculus. Science Press and CRC press INC, 1992.
[7] G.Constantini, Equations différentielles d’ordre 2, (http://bacamaths.net/).
[8] Monique Jeanblanc, Shiqi Song., Random times with given survival probability and their F-martingale decomposition formula, Stochastic Processes And their Applications, 121(2011).
[9] T.R.Bielecki, M.Jeanblanc and M.Rutkowski., Credit Rist Modelling. Osaka University Press, 2009.
[10] R.J.Elliot, M.Jeanblanc and M.Yor., On models of default risk, Mathematical Finance. 2000.
[11] I.Karatzas, Kardaras.C., The numéraire portfolioinsemimartingale financial models. Finance and Stochastics, 11(4) 447-493 (2007).
[12] T.Jeulin, M.Yor., Nouveaux résultats sur le grossissement des tribus. Ann. Scient. Ec. Norm. Sup. 4t, 11 429-443 (1978).
[13] C.Yoeurp., Décomposition des martingales locales et formules exponentielles. Séminaire de Probabilités, 10 432-480 (1976).
[14] S.W.He, J.G.Wang and J.A.Yan., Semimartingale Theory And Stochastic Calculues Science. Press, CRC, Press Inc 1992.

There are 14 citations in total.

Details

Primary Language	English
Journal Section	Articles
Authors	Fatima Benziadi This is me Abdeldjebbar Kandouci This is me
Publication Date	October 30, 2016
Submission Date	April 8, 2015
Published in Issue	Year 2016 Volume: 4 Issue: 2

Cite

APA	Benziadi, F., & Kandouci, A. (2016). The Application of Kolmogorov’s theorem in the one-default model. Mathematical Sciences and Applications E-Notes, 4(2), 71-78. https://doi.org/10.36753/mathenot.421459
AMA	Benziadi F, Kandouci A. The Application of Kolmogorov’s theorem in the one-default model. Math. Sci. Appl. E-Notes. October 2016;4(2):71-78. doi:10.36753/mathenot.421459
Chicago	Benziadi, Fatima, and Abdeldjebbar Kandouci. “The Application of Kolmogorov’s Theorem in the One-Default Model”. Mathematical Sciences and Applications E-Notes 4, no. 2 (October 2016): 71-78. https://doi.org/10.36753/mathenot.421459.
EndNote	Benziadi F, Kandouci A (October 1, 2016) The Application of Kolmogorov’s theorem in the one-default model. Mathematical Sciences and Applications E-Notes 4 2 71–78.
IEEE	F. Benziadi and A. Kandouci, “The Application of Kolmogorov’s theorem in the one-default model”, Math. Sci. Appl. E-Notes, vol. 4, no. 2, pp. 71–78, 2016, doi: 10.36753/mathenot.421459.
ISNAD	Benziadi, Fatima - Kandouci, Abdeldjebbar. “The Application of Kolmogorov’s Theorem in the One-Default Model”. Mathematical Sciences and Applications E-Notes 4/2 (October 2016), 71-78. https://doi.org/10.36753/mathenot.421459.
JAMA	Benziadi F, Kandouci A. The Application of Kolmogorov’s theorem in the one-default model. Math. Sci. Appl. E-Notes. 2016;4:71–78.
MLA	Benziadi, Fatima and Abdeldjebbar Kandouci. “The Application of Kolmogorov’s Theorem in the One-Default Model”. Mathematical Sciences and Applications E-Notes, vol. 4, no. 2, 2016, pp. 71-78, doi:10.36753/mathenot.421459.
Vancouver	Benziadi F, Kandouci A. The Application of Kolmogorov’s theorem in the one-default model. Math. Sci. Appl. E-Notes. 2016;4(2):71-8.